Written Homework 2 Due 6/19 Name: Please write complete and legible solutions to these problems, using complete sentences to explain your logic when appropriate. Show all necessary work to get to the solution; answers without work will not earn full credit. Upload one .pdf document of your solutions. Assignments that are not in .pdf format, or that are not compressed into one file will not be graded. Resources Allowed: You may consult your notes, any materials from class, and the textbook. You are encouraged to visit your instructors' office hours. If you work with a classmate, make sure that any writing or drawings you submit are your own work. Online "tutoring” sites like Chegg or Quizlett are NOT approved resources and you do not have approval to post anything from this assignment to these websites or similar. 1. (10 points) Use the given graph of g(x) to answer the following. (a) lim g(x) x+4 20 15 10 -20 -10 0 10 20 20 -5. -10- --15- -20 (c) lim g(x) (e) lim g(x) x→5- x→0 (b) lim g(x) (d) lim g(x) x+5+ x 5 1 (g) lim g(x) xx (f) lim g(x) x-4 (h) lim g(x) xx (i) What are the horizontal asymptotes of g(x)? (j) What are the vertical asymptotes of g(x)? 2. Evaluate the following limits algebraically. (a) (1 point) lim 12x-60 x 5 x²-6x+5 12x3 + 12x² (b) (1 point) lim x-1 x4 = x² X- - 3 (c) (3 points) lim x02 √√x+1 2 3. Consider the function f(x): = X (a) (1 point) Rewrite f(x) as a piecewise function. (b) (1 point) Evaluate lim f(x). x→0+ (b) (1 point) Evaluate lim f(x). x-0- (c) (2 points) Evaluate lim f(x). If the limit does not exist write, DNE. x→0 3 4. Let f(x) = x² + 1. (a) (1 point) Find the average rate of change of f(x) on [2,3]. (b) (2 points) Find the average rate of change of f(x) on [2,2+h]. (Your final answer will be in terms of h.) (c) (2 points) Use your work from part (b) and the definition of instantaneous rate of change to find the instantaneous rate of change of f(x) at x = 2. 4